Image prediction

ABSTRACT

Concepts and technologies disclosed herein are directed to image prediction. According to one aspect disclosed herein, an image prediction system can receive a training data set that includes a plurality of training images. The image prediction system can define N-dimensional feature vectors corresponding to the plurality of training images in the training data set, parameterize the N-dimensional feature vectors to obtain a plurality of parameterized curves corresponding the plurality of training images in the training data set, obtain a square root velocity representation for each parameterized curve of the plurality of parameterized curves, rescale the plurality of parameterized curves to remove scaling variability among the plurality of parameterized curves, define a pre-shape space for the plurality of parameterized curves, and obtain shape space points pertaining to each parameterized curve of the plurality of parameterized curves on a shape space that inherits a structure from the pre-shape space.

BACKGROUND

Events in life are temporal in nature and hence given a single image ora stream of images it is natural for one to ask what images are likelyto follow in the future. Such a question falls in the realm ofpredictive analytics, wherein, given data evolution models derived fromtraining datasets, one is interested in estimating how data would evolveat future time instances. While there has been a considerable amount ofwork in this area for stock pricing and natural language processingapplications, image prediction has been receiving attention onlyrecently, and it has many interesting applications.

SUMMARY

Concepts and technologies disclosed herein are directed to imageprediction. According to one aspect of the concepts and technologiesdisclosed herein, an image prediction system can receive a training dataset that includes a plurality of training images. The image predictionsystem can define N-dimensional feature vectors corresponding to theplurality of training images in the training data set, parameterize theN-dimensional feature vectors to obtain a plurality of parameterizedcurves corresponding to the plurality of training images in the trainingdata set, obtain a square root velocity representation for eachparameterized curve of the plurality of parameterized curves, rescalethe plurality of parameterized curves to remove scaling variabilityamong the plurality of parameterized curves, define a pre-shape spacefor the plurality of parameterized curves, and obtain shape space pointspertaining to each parameterized curve of the plurality of parameterizedcurves on a shape space that inherits a structure from the pre-shapespace.

In some embodiments, the image prediction system can collect a set oftest images within a time range. The image prediction system canparameterize the set of test images to obtain a test parameterizedcurve. The image prediction system can obtain a new square root velocityrepresentation point for the test parameterized curve on the shapespace.

In some embodiments, the image prediction system can determine a mean ofa plurality of training points on the shape space. Each of the pluralityof training points corresponds to the square root velocityrepresentation for each corresponding parameterized curve of theplurality of parameterized curves. The image prediction system can thendefine a tangent space around the mean and can warp the plurality oftraining points from the shape space onto the tangent space usinginverse exponential mapping. The term “warp” is used herein to encompassmapping, transforming, and/or projecting points from one space toanother. The “space” can include the shape space and the tangent space.The “points” generally refer to the data being warped. The imageprediction system can perform multi-variate statistical analysis on thetangent space to determine a most representative subset of the pluralityof training points for a given test point and can predict a test image.

In some embodiments, the image prediction system can select a topic forprediction and consider a plurality of training points pertaining to thetopic selected for prediction. The image prediction system can determinea mean of the plurality of training points on the shape space. Each ofthe plurality of training points corresponds to the square root velocityrepresentation for each corresponding parameterized curve of theplurality of parameterized curves belonging to the topic selected forprediction. The image prediction system can warp the plurality oftraining points from the shape space onto a tangent space defined at themean. The image prediction system can perform a principal componentanalysis on the tangent space to yield a principal component analysismatrix, perform dimensionality reduction by retaining eigenvectors witheigenvalues greater than 0.1, warp a test point onto the tangent spacecorresponding to the topic selected for prediction, and performdimensionality reduction using the principal component analysis matrixlearnt on the tangent space. The image prediction system can thenconsider a nearest training neighbor based upon a distance of theeigenvectors and predict a test image based upon a test parameterizedcurve corresponding to the nearest training neighbor.

In some embodiments, the image prediction system can determine a mean ofthe plurality of training points on the shape space. Each of theplurality of training points corresponds to the square root velocityrepresentation for each corresponding parameterized curve of theplurality of parameterized curves. The image prediction system can warpthe plurality of training points from the shape space onto a tangentspace defined at the mean. The image prediction system can perform aprincipal component analysis on the tangent space and warp a test pointonto the tangent space. The image prediction system can consider anearest training neighbor and predict a test image based upon a testparameterized curve corresponding to the nearest training neighbor.

In some embodiments, the image prediction system can determine a mean ofthe plurality of training points on the shape space. The imageprediction system can warp the plurality of training points from theshape space onto a tangent space defined at the mean. The imageprediction system can perform dimensionality reduction using lineardiscriminant analysis to obtain reduced dimensional vectors. The imageprediction system can consider a nearest training neighbor based upon adistance of the reduced dimensional vectors. The image prediction systemcan assign a topic label of the nearest training neighbor to a testpoint.

In some embodiments, the image prediction system can collect a testimage within a time range. The image prediction system can parameterizethe test image to obtain a test parameterized curve. The imageprediction system can obtain a new square root velocity representationpoint for the test parameterized curve on the shape space.

It should be appreciated that the above-described subject matter may beimplemented as a computer-controlled apparatus, a computer process, acomputing system, or as an article of manufacture such as acomputer-readable storage medium. These and various other features willbe apparent from a reading of the following Detailed Description and areview of the associated drawings.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intendedthat this Summary be used to limit the scope of the claimed subjectmatter. Furthermore, the claimed subject matter is not limited toimplementations that solve any or all disadvantages noted in any part ofthis disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating an overview of an approach forimage prediction, according to an illustrative embodiment of theconcepts and technologies disclosed herein.

FIG. 2 is a flow diagram illustrating aspects of a method for modelingtemporal evolution of images, according to an illustrative embodiment ofthe concepts and technologies disclosed herein.

FIG. 3 is a flow diagram illustrating aspects of a method for obtainingsquare root velocity (“SRV”) representation points for a set of testimages, according to an illustrative embodiment of the concepts andtechnologies disclosed herein.

FIG. 4 is a flow diagram illustrating aspects of a method forstatistical modeling for image prediction, according to an illustrativeembodiment of the concepts and technologies disclosed herein.

FIG. 5 is a flow diagram illustrating aspects of a method for predictingimages based upon labeled training and test points, according to anillustrative embodiment of the concepts and technologies disclosedherein.

FIG. 6 is a flow diagram illustrating aspects of a method for predictingimages based upon unlabeled training and test points, according to anillustrative embodiment of the concepts and technologies disclosedherein.

FIG. 7 is a flow diagram illustrating aspects of a method for predictingimages based upon labeled training points and unlabeled test points,according to an illustrative embodiment of the concepts and technologiesdisclosed herein.

FIG. 8 is a block diagram illustrating an example computer systemcapable of implementing aspects of the embodiments presented herein.

FIG. 9 is a block diagram illustrating an example mobile device capableof implementing aspects of the embodiments disclosed herein.

DETAILED DESCRIPTION

There are several studies in computer vision that have focused oncapturing the general notion of image dynamics. Popular among them aretracking and activity analysis, where the primary focus is on modelingtemporal evolution of objects and relevant interest regions within avideo sequence and, more recently, on estimating/predicting how theentire visual scene would transform at subsequent time instancesimmediately before or after what is contained in the video. The mainassumption in this analysis is that the images across the video sequencehave a strong notion of smoothness or continuity, which is not satisfiedby image prediction where images that would appear in the future mightnot have any common characteristics with the images currently available.There also have been other efforts on using temporal informationcontained in image sequences to supplement other visual tasks; forexample, timestamp visual metadata has been used for annotation inpersonal photo collections, geo-location estimation of a photo sequence,object and event search in online image communities as well as in scenecompletion. A non-parametric approach based on the sequential MonteCarlo to explicitly model temporal evolution of topics in web imagecollections also has been explored. While image prediction was not themain focus of this work, a related problem of sub-topic outbreakdetection where the modeled temporal evolution is used to predictvariability within a topic was explored. Also highlighted in this workwas the utility of modeling image evolution in complementing text-basedanalysis of topics and for image classification.

Another line of research ties the notion of prediction to that oftime-sensitive image retrieval. While traditional image retrievaltechniques have focused mainly on semantic similarity and featurecorrespondence, this research presented a parametric approach based onmulti-variate point processes to account for temporal similarity amongimages. More specifically, given a stream of training images until atime instant T and a future query time, the goal of this research was tocluster temporal trends amongst the training images and to suggestpossible images for the future query time that would be similar to theactual images that occurred at that time. This research also addressedprediction from the standpoint of personalizing prediction to a user'sdata. Other recent studies performed time-sensitive web image rankingand retrieval using dynamic multi-task regression, predicting evolutionof image annotations from social media to assist image retrieval, andeven estimating the age of historical photographs. A common thread amongthese approaches is to utilize temporal information as a timestampentity to accompany image semantic models, rather than explicitlymodeling the properties of temporal evolution in those image streams.

Predicting the temporal evolution of images is an interesting problemthat has applications in surveillance, content recommendation, andbehavioral analysis, among others. Given a single image or a stream ofimages with timestamps, a goal of the concepts and technologiesdisclosed herein is to predict possible images that could appear atdifferent time instances in the future. The concepts and technologiesdisclosed herein can utilize a data-driven Riemannian shape theoreticapproach to address this problem. This approach analyzes the space oftemporal evolution patterns in training image streams and performsstatistical analysis on this shape space to facilitate future imageprediction. The concepts and technologies disclosed herein consider bothdiscriminative and generative statistical analysis techniques on theshape space to accommodate cases where the training and test data mightor might not have an associated class/topic label. The concepts andtechnologies disclosed herein also provide complimentary results onpredicting images in the past—specifically, for time instances beforethe training data was acquired—and empirically analyze how theprediction accuracy varies over time.

The concepts and technologies disclosed herein for image prediction arebased, at least in part, upon spatio-temporal predictive mechanisms forsignals satisfying certain global restraints. For example, in imagesequences with smoothly changing pixel or region values, severalnon-linear, non-causal, dynamic systems with both parametric andnon-parametric characteristics have been pursued to estimate new pixelvalues that are optimal in the mean-squared error sense. However, theprimary challenge posed by the image prediction problem is that theimages that would appear in future time instances might have absolutelyno resemblance with respect to the images currently available and thus apixel or a region-level temporal modeling might not be sufficient.Furthermore, the training data to be modeled for the temporal evolutionof images need not be aligned because each training data stream mightpertain to different timescales with varying start and end timeinstances.

The concepts and technologies disclosed herein use a data-driven shapetheoretic approach in the Riemannian space such that the complexnon-linearities inherent to temporal evolution of images can be bettercaptured than the existing Euclidean counterparts. More specifically, bystarting with parametric curves fitted to features of the training imagesequence, the concepts and technologies disclosed herein work on a shapespace induced by the square root velocity (“SRV”) representation of thecurves to model the temporal evolution of the training image sequencefeatures while being robust to alignment issues. The concepts andtechnologies disclosed herein then carry out statistical computations onthe shape space in both a generative and a discriminative methodologysuch that, unlike other existing approaches, the concepts andtechnologies provide the flexibility to perform prediction when trainingand test data have topic labels, when training and test data do not havetopic labels, when the test data contains only a single image or astream of images, and when the images only have a topic label.

The concepts and technologies disclosed herein are platform independent,and as such, can be used in many context, some examples of whichinclude, but are not limited to, image search engines, image retrieval,image recommendations, and the like. For example, given a collection ofvisual content (e.g., images) consumed by one or more users, theconcepts and technologies disclosed herein can suggest what visualcontent will be interesting to the user(s) at different time instancesin the future. This also can be useful for suggesting relevant adcontent, interesting places to visit, movies, sporting events, or TVshows that might be of interest to the user(s). The concepts andtechnologies disclosed herein can be applied to surveillance as well.For example, based upon a sequence of surveillance images, the conceptsand technologies can alert surveillance agencies, emergency services,and/or the like of any untoward event that is likely to occur in thefuture, so that the event can be prevented rather than these entitiesbeing reactive to the event after it has occurred.

While the subject matter described herein may be presented, at times, inthe general context of program modules that execute in conjunction withthe execution of an operating system and application programs on acomputer system, those skilled in the art will recognize that otherimplementations may be performed in combination with other types ofprogram modules. Generally, program modules include routines, programs,components, data structures, computer-executable instructions, and/orother types of structures that perform particular tasks or implementparticular abstract data types. Moreover, those skilled in the art willappreciate that the subject matter described herein may be practicedwith other computer systems, including hand-held devices, vehicles,wireless devices, multiprocessor systems, distributed computing systems,microprocessor-based or programmable consumer electronics,minicomputers, mainframe computers, routers, switches, other computingdevices described herein, and the like.

In the following detailed description, references are made to theaccompanying drawings that form a part hereof, and in which are shown byway of illustration specific embodiments or examples. Referring now tothe drawings, in which like numerals represent like elements throughoutthe several figures, aspects of image prediction will be described.

Referring now to FIG. 1, a block diagram illustrating an overview 100 ofan approach for image prediction will be described, according to anillustrative embodiment of the concepts and technologies disclosedherein. It should be understood that the overview 100 and the variouscomponents thereof have been greatly simplified for purposes ofdiscussion. Accordingly, additional or alternative components of theoverview 100 can be made available without departing from theembodiments of the concepts and technologies described herein.

The illustrated overview 100 includes an image prediction system 102that utilizes training data 104, including a plurality of trainingimages 106A-106P (“training images 106”), within a given time intervalbetween a time T₁ 108A and a time T₂ 108B and corresponding to topics ofinterest 110A-110B (“topics or topic labels 110 ”) to model a temporalevolution of the training images 106 using a shape space 112 induced bythe square root velocity (“SRV”) representation of parametric curves114A-114D to enable prediction of one or more past images 116A-116H(“past images 116”) and/or a plurality of future images 118A-118H(“future images 118”). The training images 106 are divided into fourtraining image streams, shown here row-wise, with the first two rows120A, 120B belonging to a first topic 110A, and the last two rows 120C,120D belonging to a second topic 110B. The training image streams areshown having the same time interval between the time T₁ 108A and thetime T₂ 108B. In some embodiments, the training image streams can havedifferent start and/or end time instances and/or a different samplingfrequency. The shape space 112 includes shape space points 122A-122Dcorresponding to the training image streams in the rows 120A-120D,respectively. Given test data (not shown)—for example, a single testimage, a set (or sequence) of images, or just a topic label—in the timeinterval between the time T₁ 108A and the time T₂ 108B, the imageprediction system 102 can predict one or more images outside of the timeinterval (i.e., the past image(s) 116 and/or the future image(s) 118)using a learned prediction model 124 created based upon the trainingdata 104.

The concepts and technologies disclosed here provide a data-driven shapetheoretic approach in the Riemannian space such that the complexnon-linearities inherent to temporal evolution of images can be bettercaptured than the existing Euclidean counterparts. More specifically, bystarting with the parametric curves 114A-114D fitted to common featuresof the training images 106, the image prediction system 102 utilizes theshape space 112 induced by the SRV representation of the parametriccurves 114A-114D to model the temporal evolution of the parametriccurves 114A-114D while being robust to alignment issues. The imageprediction system 102 disclosed herein then carries out statisticalcomputations on the shape space 112 in both a generative anddiscriminative sense such that, unlike other existing approaches, theimage prediction system 102 provides the flexibility to performprediction when training and test data have labels or not, and when thetest data contains only a single image or a stream of images, or just atopic label 110.

It should be understood that some implementations of the overview 100can include a different number of image prediction systems 102, trainingdata 104, training images 106, times 108, topics 110, shape spaces 112,past images 116, future images 118, rows 120 (represented by imagestreams), parametric curves 114, shape space points 122, predictionmodels 124, or any combination thereof. Thus, the illustrated embodimentshould be understood as being illustrative, and should not be construedas being limiting in any way.

Turning now to FIG. 2, a flow diagram illustrating aspects of a method200 for modeling temporal evolution of images, such as the trainingimages 106, will be described, according to an illustrative embodiment.It should be understood that the operations of the methods disclosedherein are not necessarily presented in any particular order and thatperformance of some or all of the operations in an alternative order(s)is possible and is contemplated. The operations have been presented inthe demonstrated order for ease of description and illustration.Operations may be added, omitted, and/or performed simultaneously,without departing from the scope of the concepts and technologiesdisclosed herein.

It also should be understood that the methods disclosed herein can beended at any time and need not be performed in its entirety. Some or alloperations of the methods, and/or substantially equivalent operations,can be performed by execution of computer-readable instructions includedon a computer storage media, as defined herein. The term“computer-readable instructions,” and variants thereof, as used herein,is used expansively to include routines, applications, applicationmodules, program modules, programs, components, data structures,algorithms, and the like. Computer-readable instructions can beimplemented on various system configurations including single-processoror multiprocessor systems or devices, minicomputers, mainframecomputers, personal computers, hand-held computing devices,microprocessor-based, programmable consumer electronics, combinationsthereof, and the like.

Thus, it should be appreciated that the logical operations describedherein are implemented (1) as a sequence of computer implemented acts orprogram modules running on a computing system and/or (2) asinterconnected machine logic circuits or circuit modules within thecomputing system. The implementation is a matter of choice dependent onthe performance and other requirements of the computing system.Accordingly, the logical operations described herein are referred tovariously as states, operations, structural devices, acts, or modules.These states, operations, structural devices, acts, and modules may beimplemented in software, in firmware, in special purpose digital logic,and any combination thereof. As used herein, the phrase “cause aprocessor to perform operations” and variants thereof is used to referto causing one or more processors of one or more computing systemsand/or devices disclosed herein, such as the image prediction system102, to perform operations.

For purposes of illustrating and describing some of the concepts of thepresent disclosure, operations of the methods disclosed herein aredescribed as being performed, at least in part, by the image predictionsystem 102, via execution, by one or more processors, of one or moresoftware modules, which can be used to implement the prediction model124. It should be understood that additional and/or alternative devicesand/or network nodes can provide the functionality described herein viaexecution of one or more modules, applications, and/or other software.Thus, the illustrated embodiments are illustrative, and should not beviewed as being limiting in any way.

The methods disclosed herein will be described in context of thefollowing: Let {x_(i)}_(i) denote the training data 104, where eachx_(i) consists of a stream (e.g., a set or a sequence) of images, suchas the training images 106, taken within a time interval, such asbetween T₁ 108A and T₂ 108B. Each x_(i) also can have an associatedtopic label y_(i), such as the topic label 110, pertaining to one of Mdifferent topics that the training images 106 contained thereincorrespond thereto. As a non-limiting example, x_(i) can be a set ofimages retrieved from a news website within the time interval between T₁108A and T₂ 108B when searched for a particular topic keyword such as“football.” Test data {x _(i)}_(i) corresponding to all M topics, suchas the topics 110, also is provided. Each x _(i) contains a set ofimages pertaining to (i) timestamps between T₁ 108A and T₂ 108B, denotedby x _(i) ^(a), and (ii) timestamps before T₁ 108A and T₂ 108B, denotedby x _(i) ^(b).

Given this context, a goal of the concepts and technologies disclosedherein is to model temporal evolution of the training data {x_(i)}_(i)104, such that, given a test image set x _(i) ^(a), the images predictedusing the prediction model 124 for a timeframe before T₁ 108A and T₂108B, say x*_(i), are similar to the actual test images present in thattimeframe, namely x _(i) ^(b). The concepts and technologies disclosedherein also address scenarios where x _(i) ^(a) contains only a singletest image and when only the topic label of the images is available tobe predicted without any image(s) for x _(i) ^(a). This goal is metusing a two-stage approach by (i) modeling temporal evolution within thetraining data using principles from Riemannian shape analysis and (ii)utilizing statistical tools on the shape space 112 to predict futureimages 118 and past images 116, in both a generative and discriminativemanner depending on the availability of topic labels for training andtest data. Towards this end, the method 200 is described under theassumption that the images are represented by an N-dimensional featurevector, the choice of which choice depends on a sample dataset.

The method 200 will be described with reference to FIG. 2 and furtherreference to FIG. 1. The method 200 begins and proceeds to operation202, where, for each stream of images in a training data set (e.g., thetraining data 104), the image prediction system 102 can defineN-dimensional feature vectors corresponding to the images (e.g., thetraining images 106) contained therein. From operation 202, the method200 proceeds to operation 204, where the image prediction system 102parameterizes the feature vectors using a Gaussian distribution functiong_(i) to obtain a collection of parameterized curves {g_(i)}_(i) (e.g.,the parameterized curves 114) corresponding to the training data 104{x_(i)}_(i). It should be understood that the image prediction system102 can parameterize the feature vectors using other functions.Accordingly, the use of a Gaussian distribution function is oneillustrative embodiment and should not be construed as being limiting inany way. After obtaining a collection of parameterized curves 114{g_(i)}_(i) corresponding to the training data 104 {x_(i)}, the imageprediction system 102 can model the temporal trends contained therein tocreate the prediction model 124 to enable prediction. However, theinformation contained within the collection of parameterized curves 114{g_(i)}_(i) do not need to be aligned. This is because the images (e.g.,the training images 106) across the training data 104 {x_(i)}_(i),although belonging to time instances between T₁ 108A and T₂ 108B, mightnot correspond to the same start time and/or end time. Moreover, thesampling interval between the images also can be different. One way toaccommodate for this is to normalize the parameterized curves 114{g_(i)}_(i).

From operation 204, the method 200 proceeds to operation 206, where, foreach parameterized curve 114 in the collection of parameterized curves114 {g_(i)}_(i), the image prediction system 102 obtains its SRVrepresentation G_(i). Given a parameterized curve g_(i) (g_(i):D→

^(n)) where D is a certain domain for parameterization, the SRVrepresentation G_(i) is obtained through continuous mapping

${G_{i}(t)} = \frac{\left. g_{\iota}\overset{.}{(}t \right)}{\sqrt{\left. g_{\iota}\overset{.}{(}t \right)}}$where ∥.∥ is the Euclidean 2-norm in

^(n). From operation 206, the method 200 proceeds to operation 208,where the image prediction system 102 rescales the parameterized curves114 to remove scaling variability among the parameterized curves 114such that all of the parameterized curves 114 are of length 2π. Thus,the SRV functions associated with the parameterized curves 114 areelements of a hypersphere in the Hilbert manifold

² (D,

^(n)). From operation 208, the method 200 proceeds to operation 210,where the image prediction system 102 defines a pre-shape space, C, foreach of the parameterized curves 114. From operation 210, the method 200proceeds to operation 212, where the image prediction system 102 canthen account for other normalizing transformations, such as translation,rotation, and re-parameterization, to obtain points (e.g., the shapespace points 122) pertaining to SRV representations G_(i)'s on theresultant shape space S (e.g., the shape space 112) that inherits theRiemannian structure from C. From operation 212, the method 200 proceedsto operation 214. The method 200 ends at operation 214.

Turning now to FIG. 3, a flow diagram illustrating aspects of a method300 for obtaining SRV representation points for a set of test imageswill be described, according to an illustrative embodiment of theconcepts and technologies disclosed herein. The method 300 begins andproceeds to operation 302, wherein, given a set of test images x _(i)^(a) collected within a time range (e.g., between T₁ 108A and T₂ 108B),the image prediction system 102 can parameterize the set of test imagesx _(i) ^(a) with a Gaussian function g _(i) to obtain parameterizedcurves. From operation 302, the method 300 proceeds to operation 304,where, for each parameterized curve, the image prediction system 102obtains an SRV representation point G _(i) on the shape space 112 S.Such a representation enables systematic analysis for modeling points onthe shape space 112 S using tools that account for the geometry of theshape space 112 S. From operation 304, the method 300 proceeds tooperation 306.

Turning now to FIG. 4, a flow diagram illustrating aspects of a method400 for statistical modeling for image prediction will be described,according to an illustrative embodiment of the concepts and technologiesdisclosed herein. The method 400 describes statistical modeling on theshape space 112 S to transfer temporal evolution patterns conveyed bythe training points {G_(i)}_(i) onto the test point G _(i) and topredict relevant test images x*_(i) occurring before T₁ 108A and afterT₂ 108B that should ideally be similar to the ground truth contained inx _(i) ^(b).

The method 400 begins and proceeds to operation 402, where the imageprediction system 102 determines the mean of the training points. Insome embodiments, the image prediction system 102 can determine the meanof the training points on the shape space 112 S using the Karcher mean,which requires a computing distance between points on the shape space112 S. The shortest distance between a pair of points is given by thegeodesic distance. From operation 402, the method 400 proceeds tooperation 404, where the image prediction system 102 defines a tangentspace T around the mean computed at operation 402. From operation 404,the method 400 proceeds to operation 406, where the image predictionsystem 102 warps the training points {G_(i)}_(i) from the shape space112 S to the tangent space T using inverse exponential mapping. Fromoperation 406, the method 400 proceeds to operation 408, where the imageprediction system 102 performs multi-variate statistical analysis on thetangent space T to determine the most representative subset of thetraining points {G_(i)}_(i) for a given test point G _(i). Fromoperation 408, the method 400 proceeds to operation 410, where the imageprediction system 102 uses the subset to predict relevant test imagesx*_(i). From operation 410, the method 400 proceeds to operation 412.The method 400 ends at operation 412.

To compute the geodesic distance, the image prediction system 102considers the pre-shape space C where, given two points G₀ and G₁ and aparameterized path ∝: [0, 1]→C such that ∝(0)=G₀ and ∝(1)=G₁, the lengthof ∝ is defined as L[∝]=∫₀ ¹

{dot over (∝)} (t), {dot over (∝)} (t)

^(1/2) dt. ∝ is a length-minimizing geodesic if L [∝] achieves theinfimum over all paths, and the length of this geodesic becomes adistance

${d_{c}\left( {G_{0},G_{1}} \right)} = {\propto {\text{:}\mspace{14mu}\begin{matrix}\inf \\{{{\left. \left\lbrack {0,1} \right\rbrack\rightarrow C \right.❘{\propto (0)}} = G_{0}},{{\propto (1)} = {G_{1}^{L{\lbrack \propto \rbrack}}.}}}\end{matrix}}}$Consequently, the geodesics in C that are perpendicular to all theorbits meet in the pre-shape C, and the geodesic distance between anytwo points in the shape space 112 S is given by

${d_{s}\left( {\left\lbrack G_{0} \right\rbrack,\left\lbrack G_{1} \right\rbrack} \right)} = {{\min\limits_{{\overset{\_}{G}}_{1} \in {\lbrack G_{1}\rbrack}}{d_{c}\left( {G_{0},{\overset{\_}{G}}_{1}} \right)}} = {\begin{matrix}\inf \\{\left( {\gamma,0} \right) \in {\Gamma \times {{SO}(n)}}}\end{matrix}{{d_{c}\left( {G_{0},{{O\left( {G_{1} \cdot \gamma} \right)}\sqrt{\overset{.}{\gamma}}}} \right)}.}}}$The orbit of G₀ ∈ C is given by, [G₀]={O(G₀ ∘ γ)√{square root over ({dotover (γ)})}|(γ, O) ∈ Γ×SO(n)} where rotation of the curve g₀ pertainingto G₀ is handled by the actions of the special orthogonal group of n×nmatrices SO(n), and its re-parameterization by the composition G₀ ∘ γ, γ∈ Γ, which is the set of all orientation preserving diffeomorphisms ofD. The Karcher mean μ is then given by

$\mu = {\arg\;{\min\limits_{{\lbrack G\rbrack} \in S}{\sum\limits_{i}{{d_{S}\left( {\lbrack G\rbrack,\left\lbrack G_{i} \right\rbrack} \right)}^{2}.}}}}$Once μ is determined, the image prediction system 102 can map the SRVrepresentations G_(i)'s to the tangent space T using the mappingv_(i)=exp_(μ) ⁻¹ ([G_(i)]∈T_(μ)(S)), where exp_(μ) ⁻¹ is the inverseexponential map defined at μ.

Additional methods for predicting images based upon the concepts andtechnologies described above will now be described based upon whetherthe training points {G_(i)}_(i) and the test point G _(i) have topiclabels 110 or not. Turning first to FIG. 5, a flow diagram illustratingaspects of a method 500 for predicting images based upon labeledtraining points and test points will be described, according to anillustrative embodiment of the concepts and technologies disclosedherein. The method 500 begins and proceeds to operation 502, where theimage prediction system 102 selects a topic 110 for prediction. Theimage prediction system 102 can perform the operations of the method 500for each of the M topics in a given data set. From operation 502, themethod 500 proceeds to operation 504, where the image prediction system102 considers training points pertaining to the topic 110 selected forprediction. From operation 504, the method 500 proceeds to operation506, where the image prediction system 102 determines the mean of thetraining points pertaining to the topic selected for prediction. In someembodiments, the image prediction system 102 can compute the mean as aKarcher mean.

From operation 506, the method 500 proceeds to operation 508, where theimage prediction system 102 warps the training points onto the tangentspace defined at the mean. From operation 508, the method 500 proceedsto operation 510, where the image prediction system 102 performsprincipal component analysis (“PCA”) on the tangent space. This capturesholistic trends of temporal evolution pertaining to that topic. Fromoperation 510, the method 500 proceeds to operation 512, where the imageprediction system 102 performs dimensionality reduction by retainingthose eigenvectors with eigenvalues greater than 0.1.

From operation 512, the method 500 proceeds to operation 514, where, fora given test point, the image prediction system 102 warps the test pointto the tangent space T corresponding to its topic 110. From operation514, the method 500 proceeds to operation 516, where the imageprediction system 102 performs dimensionality reduction using the PCAmatrix learnt on that tangent space T.

From operation 516, the method 500 proceeds to operation 518, where theimage prediction system 102 considers the nearest k training neighbors,based upon the

₂ distance of the reduced dimensional vectors. From operation 518, themethod 500 proceeds to operation 520, where the image prediction system102 performs prediction based upon the parametric curves g_(i)'scorresponding to those neighbors. More specifically, the imageprediction system 102 can sample temporally along each of the curvesg_(i)'s outside of the time interval between T₁ 108A and T2 108B toobtain a set of N-dimensional feature vectors that forms a predictionoutput x*_(i). The prediction output can then be compared with thefeature vectors contained in the ground truth x _(i) ^(b) to obtain aprediction accuracy. From operation 520, the method 500 proceeds tooperation 522, where the method 500 ends.

Turning now to FIG. 6, a flow diagram illustrating aspects of a method600 for predicting images based upon unlabeled training and test pointswill be described, according to an illustrative embodiment of theconcepts and technologies disclosed herein. The method 600 begins andproceeds to operation 602, where the image prediction system 102determines the mean for all training points. In some embodiments, theimage prediction system 102 can compute the mean as a Karcher mean.

From operation 602, the method 600 proceeds to operation 604, where theimage prediction system 102 warps the training points onto the tangentspace T defined at the mean. From operation 604, the method 600 proceedsto operation 606, where the image prediction system 102 performs PCA onthe tangent space T. From operation 606, the method 600 proceeds tooperation 608, where the image prediction system 102 warps the testpoint to the tangent space T From operation 608, the method 600 proceedsto operation 610, where the image prediction system 102 considers thenearest k training neighbors based upon the

₂ distance of the reduced dimensional vectors. From operation 610, themethod 600 proceeds to operation 612, where the image prediction system102 performs prediction based upon parametric curves g_(i)'scorresponding to those neighbors. More specifically, the imageprediction system 102 can sample temporally along each of the parametriccurves g_(i)'s outside of the time interval between T₁ 108A and T₂ 108Bto obtain a set of N-dimensional feature vectors that forms a predictionoutput x*_(i). The prediction output can then be compared with thefeature vectors contained in the ground truth x _(i) ^(b) to obtain aprediction accuracy. From operation 612, the method 600 proceeds tooperation 614, where the method 600 ends.

Turning now to FIG. 7, a flow diagram illustrating aspects of a method700 for predicting images based upon labeled training points and anunlabeled test point will be described, according to an illustrativeembodiment of the concepts and technologies disclosed herein. The method700 begins and proceeds to operation 702, where the image predictionsystem 102 determines the mean for training points from all topics 110.In some embodiments, the image prediction system 102 can compute themean as the Karcher mean.

From operation 702, the method 700 proceeds to operation 704, where theimage prediction system 102 warps the training points onto the tangentspace T defined at the mean. From operation 704, the method 700 proceedsto operation 706, where the image prediction system 102 performsdimensionality reduction using linear discriminant analysis (“LDA”).From operation 706, the method 700 proceeds to operation 708, where theimage prediction system 102 performs the same procedure as set forthabove for an unlabeled test point and identifies the nearest trainingneighbor based upon the

₂ distance of the reduced dimensional vectors. From operation 708, themethod 700 proceeds to operation 710, where the image prediction system102 assigns the topic label 110 of the nearest training neighbor to thetest point. From operation 710, the method 700 proceeds to operation712. The method 700 ends at operation 712.

The methods 500, 600, 700 can be applied to multiple test images or asingle test image. The scenario in which a single test image, in thetime interval between T₁ 108A and T₂ 108B, instead of a set of images inx _(i) ^(a) will now be described. An issue with this scenario is thatthe temporal evolution g _(i) cannot be captured from a single image inthe pursuit of finding nearest training neighbors using statistics onthe shape space S 112. The image prediction system 102 can adopt thestrategy of first selecting parametric curves g_(i)'s that have imagesmost similar to the test image. For each parametric curve g_(i), theimage prediction system 102 can assign the minimum of the

₂ distance computed between the feature vector of the test image withthe feature vector of each image contained in x_(i). The imageprediction system 102 can then sort the parametric curves g_(i)'s inincreasing order of the

₂ distance, select the top 50% of the parametric curves g_(i)'s, andthen the image prediction system 102 can pursue statistics on therespective parametric curves G_(i)'s to perform prediction.

For the case in which the training and test data are labeled (e.g., themethod 500), the image prediction system 102 can shortlist the top 50%of parametric curves g_(i)'s corresponding to the test data topic,compute the mean of the corresponding G_(i)'s, and perform PCA on thetangent space T. The image prediction system 102 can then obtain the knearest training neighbors whose PCA-based reduced dimensional vectorsare closest to the mean of all such reduced dimension vectors and usethe corresponding parametric curves g_(i)'s to perform prediction asdescribed above. For the case in which the training and test data areunlabeled (e.g., the method 600), the image prediction system 102 canperform operations similar to those describe above for the case in whichthe training and test data are labeled but for shortlisting the top 50%parametric curves g_(i)'s from all topics, since the training and testdata are not labeled. For the case in which training data is labeled andtest data is unlabeled, the image prediction system 102 can identify atest topic label by considering the top 50% of the parametric curvesg_(i)'s from all topics, compute the mean of the corresponding G_(i)'s,and perform LDA on the tangent space T as described above for the casein which training data is labeled and test data is unlabeled. The imageprediction system 102 can then identify the LDA-based reduced dimensionvector that is closest to the mean of all such reduced dimensionvectors, assign the corresponding topic label to the test image, andthen follow steps described above for the case in which the training andtest data are labeled to perform prediction for the test image. Tosummarize, the image prediction system 102 can utilize image similarityas the cue to identify closest training points with which the imageprediction system 102 can subsequently model the temporal evolutionthereof to perform prediction for the test image.

Prediction scenarios might arise wherein the goal is to predict imagespertaining to a topic in general, as opposed to being given a set oftest images or a single test image in x _(i) ^(a) and asked to makepredictions based that image or set of images. Given training data{x_(i)}_(i) with topic labels, the image prediction system 102 canidentify the subset of training points that are best suited forprediction. The image prediction system 102 can implement thisidentification using a clustering approach, and the operations of themethod 500 can be followed to project the training points correspondingto the test topic onto its tangent space T. Afterwards, the imageprediction system 102 can perform k-means clustering on the tangentspace T. The image prediction system 102 can then use the parametriccurves g_(i)'s corresponding to the training points closest to each ofthe k cluster centers to perform prediction as described above.

It should be understood that the techniques utilized by the imageprediction system 102 to perform the operations of the methods 500, 600,700 and the additional prediction scenarios described herein above aremerely illustrative examples of some of the statistical tools that canbe utilized by the image prediction system 120. Those skilled in the artwill appreciate the applicability of other statistical tools that can beimplemented by the image prediction system 102 to achieve the same orsimilar results to those described herein. Accordingly, the use ofstatistical tools such as PCA, LDA and k-means should not be construedas being limiting in any way.

FIG. 8 is a block diagram illustrating a computer system 800 configuredto perform various operations disclosed herein. The computer system 800includes a processing unit 802, a memory 804, one or more user interfacedevices 806, one or more input/output (“I/O”) devices 808, and one ormore network devices 810, each of which is operatively connected to asystem bus 812. The system bus 812 enables bi-directional communicationbetween the processing unit 802, the memory 804, the user interfacedevices 806, the I/O devices 808, and the network devices 810. In someembodiments, the image prediction system 102 or one or more componentsthereof can be configured, at least in part, like the computer system800. It should be understood, however, that one or more of theseelements may include additional functionality or include lessfunctionality than now described.

The processing unit 802 may be a standard central processor thatperforms arithmetic and logical operations, a more specific purposeprogrammable logic controller (“PLC”), a programmable gate array, orother type of processor known to those skilled in the art and suitablefor controlling the operation of the computer system 800. Processingunits are generally known, and therefore are not described in furtherdetail herein.

The memory 804 communicates with the processing unit 802 via the systembus 812. In some embodiments, the memory 804 is operatively connected toa memory controller (not shown) that enables communication with theprocessing unit 802 via the system bus 812. The illustrated memory 804includes an operating system and one or more applications 816.

The operating system 814 can include, but is not limited to, members ofthe WINDOWS, WINDOWS CE, WINDOWS MOBILE, and/or WINDOWS PHONE familiesof operating systems from MICROSOFT CORPORATION, the LINUX family ofoperating systems, the SYMBIAN family of operating systems from SYMBIANLIMITED, the BREW family of operating systems from QUALCOMM CORPORATION,the MAC OS and/or iOS families of operating systems from APPLE INC., theFREEBSD family of operating systems, the SOLARIS family of operatingsystems from ORACLE CORPORATION, other operating systems such asproprietary operating systems, and the like.

The user interface devices 806 may include one or more devices withwhich a user accesses the computer system 800. The user interfacedevices 806 may include, but are not limited to, computers, servers,personal digital assistants, telephones (e.g., cellular, IP, orlandline), or any suitable computing devices. The I/O devices 808 enablea user to interface with the program modules. In one embodiment, the I/Odevices 808 are operatively connected to an I/O controller (not shown)that enables communication with the processing unit 802 via the systembus 812. The I/O devices 808 may include one or more input devices, suchas, but not limited to, a keyboard, a mouse, a touchscreen, or anelectronic stylus. Further, the I/O devices 808 may include one or moreoutput devices, such as, but not limited to, a display screen or aprinter.

The network devices 810 enable the computer system 800 to communicatewith other networks or remote systems via a network 818. Examples of thenetwork devices 810 include, but are not limited to, a modem, a radiofrequency (“RF”) or infrared (“IR”) transceiver, a telephonic interface,a bridge, a router, or a network card. The network 818 may include awireless network such as, but not limited to, a wireless local areanetwork (“WLAN”) such as a WI-FI network, a wireless wide area network(“WWAN”), a wireless personal area network (“WPAN”) such as BLUETOOTH,or a wireless metropolitan area network (“WMAN”). Alternatively, thenetwork 818 may be a wired network such as, but not limited to, a WANsuch as the Internet, a LAN such as the Ethernet, a wired PAN, or awired MAN.

Turning now to FIG. 9, an illustrative mobile device 900 and componentsthereof will be described. In some embodiments, the image predictionsystem 102 is configured the same as or similar to the mobile device900. While connections are not shown between the various componentsillustrated in FIG. 9, it should be understood that some, none, or allof the components illustrated in FIG. 9 can be configured to interactwith one another to carry out various device functions. In someembodiments, the components are arranged so as to communicate via one ormore busses (not shown). Thus, it should be understood that FIG. 9 andthe following description are intended to provide a generalunderstanding of a suitable environment in which various aspects ofembodiments can be implemented, and should not be construed as beinglimiting in any way.

As illustrated in FIG. 9, the mobile device 900 can include a display902 for displaying data. According to various embodiments, the display902 can be configured to display network connection information, variousgraphical user interface (“GUI”) elements, text, images, video, virtualkeypads and/or keyboards, messaging data, notification messages,metadata, Internet content, device status, time, date, calendar data,device preferences, map and location data, combinations thereof, and/orthe like. The mobile device 900 also can include a processor 904 and amemory or other data storage device (“memory”) 906. The processor 904can be configured to process data and/or can execute computer-executableinstructions stored in the memory 906. The computer-executableinstructions executed by the processor 904 can include, for example, anoperating system 908, one or more applications 910, othercomputer-executable instructions stored in the memory 906, or the like.In some embodiments, the applications 910 also can include a UIapplication (not illustrated in FIG. 9).

The UI application can interface with the operating system 908 tofacilitate user interaction with functionality and/or data stored at themobile device 900 and/or stored elsewhere. In some embodiments, theoperating system 908 can include a member of the SYMBIAN OS family ofoperating systems from SYMBIAN LIMITED, a member of the WINDOWS MOBILEOS and/or WINDOWS PHONE OS families of operating systems from MICROSOFTCORPORATION, a member of the PALM WEBOS family of operating systems fromHEWLETT PACKARD CORPORATION, a member of the BLACKBERRY OS family ofoperating systems from RESEARCH IN MOTION LIMITED, a member of the IOSfamily of operating systems from APPLE INC., a member of the ANDROID OSfamily of operating systems from GOOGLE INC., and/or other operatingsystems. These operating systems are merely illustrative of somecontemplated operating systems that may be used in accordance withvarious embodiments of the concepts and technologies described hereinand therefore should not be construed as being limiting in any way.

The UI application can be executed by the processor 904 to aid a user indata communications, entering/deleting data, entering and setting userIDs and passwords for device access, configuring settings, manipulatingcontent and/or settings, multimode interaction, interacting with otherapplications 910, and otherwise facilitating user interaction with theoperating system 908, the applications 910, and/or other types orinstances of data 912 that can be stored at the mobile device 900.

The applications 910, the data 912, and/or portions thereof can bestored in the memory 906 and/or in a firmware 914, and can be executedby the processor 904. The firmware 914 also can store code for executionduring device power up and power down operations. It can be appreciatedthat the firmware 914 can be stored in a volatile or non-volatile datastorage device including, but not limited to, the memory 906 and/or aportion thereof.

The mobile device 900 also can include an input/output (“I/O”) interface916. The I/O interface 916 can be configured to support the input/outputof data such as location information, presence status information, userIDs, passwords, and application initiation (start-up) requests. In someembodiments, the I/O interface 916 can include a hardwire connectionsuch as a universal serial bus (“USB”) port, a mini-USB port, amicro-USB port, an audio jack, a PS2 port, an IEEE 1394 (“FIREWIRE”)port, a serial port, a parallel port, an Ethernet (RJ45) port, an RJ11port, a proprietary port, combinations thereof, or the like. In someembodiments, the mobile device 900 can be configured to synchronize withanother device to transfer content to and/or from the mobile device 900.In some embodiments, the mobile device 900 can be configured to receiveupdates to one or more of the applications 910 via the I/O interface916, though this is not necessarily the case. In some embodiments, theI/O interface 916 accepts I/O devices such as keyboards, keypads, mice,interface tethers, printers, plotters, external storage,touch/multi-touch screens, touch pads, trackballs, joysticks,microphones, remote control devices, displays, projectors, medicalequipment (e.g., stethoscopes, heart monitors, and other health metricmonitors), modems, routers, external power sources, docking stations,combinations thereof, and the like. It should be appreciated that theI/O interface 916 may be used for communications between the mobiledevice 900 and a network device or local device.

The mobile device 900 also can include a communications component 918.The communications component 918 can be configured to interface with theprocessor 904 to facilitate wired and/or wireless communications withone or more networks described herein. In some embodiments, thecommunications component 918 includes a multimode communicationssubsystem for facilitating communications via the cellular network andone or more other networks.

The communications component 918, in some embodiments, includes one ormore transceivers. The one or more transceivers, if included, can beconfigured to communicate over the same and/or different wirelesstechnology standards with respect to one another. For example, in someembodiments, one or more of the transceivers of the communicationscomponent 918 may be configured to communicate using Global System forMobile communications (“GSM”), Code Division Multiple Access (“CDMA”)CDMAONE, CDMA2000, Long-Term Evolution (“LTE”), and various other 2G,2.5G, 3G, 4G, 5G, and greater generation technology standards. Moreover,the communications component 918 may facilitate communications overvarious channel access methods (which may or may not be used by theaforementioned standards) including, but not limited to, time-divisionmultiple access (“TDMA”), frequency-division multiple access (“FDMA”),wideband CDMA (“W-CDMA”), orthogonal frequency-division multiplexing(“OFDM”), space-division multiple access (“SDMA”), and the like.

In addition, the communications component 918 may facilitate datacommunications using General Packet Radio Service (“GPRS”), EnhancedData rates for Global Evolution (“EDGE”), the High-Speed Packet Access(“HSPA”) protocol family including High-Speed Downlink Packet Access(“HSDPA”), Enhanced Uplink (“EUL”) or otherwise termed High-Speed UplinkPacket Access (“HSUPA”), evolved HSPA (“HSPA+”), and various othercurrent and future wireless data access standards. In the illustratedembodiment, the communications component 918 can include a firsttransceiver (“TxRx”) 920A that can operate in a first communicationsmode (e.g., GSM). The communications component 918 also can include anN^(th) transceiver (“TxRx”) 920N that can operate in a secondcommunications mode relative to the first transceiver 920A (e.g., UMTS).While two transceivers 920A-920N (hereinafter collectively and/orgenerically referred to as “transceivers 920”) are shown in FIG. 9, itshould be appreciated that less than two, two, and/or more than twotransceivers 920 can be included in the communications component 918.

The communications component 918 also can include an alternativetransceiver (“Alt TxRx”) 922 for supporting other types and/or standardsof communications. According to various contemplated embodiments, thealternative transceiver 922 can communicate using various communicationstechnologies such as, for example, WI-FI, WIMAX, BLUETOOTH, infrared,infrared data association (“IRDA”), near field communications (“NFC”),other RF technologies, combinations thereof, and the like. In someembodiments, the communications component 918 also can facilitatereception from terrestrial radio networks, digital satellite radionetworks, internet-based radio service networks, combinations thereof,and the like. The communications component 918 can process data from anetwork such as the Internet, an intranet, a broadband network, a WI-FIhotspot, an Internet service provider (“ISP”), a digital subscriber line(“DSL”) provider, a broadband provider, combinations thereof, or thelike.

The mobile device 900 also can include one or more sensors 924. Thesensors 924 can include temperature sensors, light sensors, air qualitysensors, movement sensors, accelerometers, magnetometers, gyroscopes,infrared sensors, orientation sensors, noise sensors, microphonesproximity sensors, combinations thereof, and/or the like. Additionally,audio capabilities for the mobile device 900 may be provided by an audioI/O component 926. The audio I/O component 926 of the mobile device 900can include one or more speakers for the output of audio signals, one ormore microphones for the collection and/or input of audio signals,and/or other audio input and/or output devices.

The illustrated mobile device 900 also can include a subscriber identitymodule (“SIM”) system 928. The SIM system 928 can include a universalSIM (“USIM”), a universal integrated circuit card (“UICC”) and/or otheridentity devices. The SIM system 928 can include and/or can be connectedto or inserted into an interface such as a slot interface 930. In someembodiments, the slot interface 930 can be configured to acceptinsertion of other identity cards or modules for accessing various typesof networks. Additionally, or alternatively, the slot interface 930 canbe configured to accept multiple subscriber identity cards. Becauseother devices and/or modules for identifying users and/or the mobiledevice 900 are contemplated, it should be understood that theseembodiments are illustrative, and should not be construed as beinglimiting in any way.

The mobile device 900 also can include an image capture and processingsystem 932 (“image system”). The image system 932 can be configured tocapture or otherwise obtain photos, videos, and/or other visualinformation. As such, the image system 932 can include cameras, lenses,charge-coupled devices (“CCDs”), combinations thereof, or the like. Themobile device 900 may also include a video system 934. The video system934 can be configured to capture, process, record, modify, and/or storevideo content. Photos and videos obtained using the image system 932 andthe video system 934, respectively, may be added as message content toan MMS message, email message, and sent to another device. The videoand/or photo content also can be shared with other devices via varioustypes of data transfers via wired and/or wireless communication devicesas described herein.

The mobile device 900 also can include one or more location components936. The location components 936 can be configured to send and/orreceive signals to determine a geographic location of the mobile device900. According to various embodiments, the location components 936 cansend and/or receive signals from global positioning system (“GPS”)devices, assisted-GPS (“A-GPS”) devices, WI-FI/WIMAX and/or cellularnetwork triangulation data, combinations thereof, and the like. Thelocation component 936 also can be configured to communicate with thecommunications component 918 to retrieve triangulation data fordetermining a location of the mobile device 900. In some embodiments,the location component 936 can interface with cellular network nodes,telephone lines, satellites, location transmitters and/or beacons,wireless network transmitters and receivers, combinations thereof, andthe like. In some embodiments, the location component 936 can includeand/or can communicate with one or more of the sensors 924 such as acompass, an accelerometer, and/or a gyroscope to determine theorientation of the mobile device 900. Using the location component 936,the mobile device 900 can generate and/or receive data to identify itsgeographic location, or to transmit data used by other devices todetermine the location of the mobile device 900. The location component936 may include multiple components for determining the location and/ororientation of the mobile device 900.

The illustrated mobile device 900 also can include a power source 938.The power source 938 can include one or more batteries, power supplies,power cells, and/or other power subsystems including alternating current(“AC”) and/or direct current (“DC”) power devices. The power source 938also can interface with an external power system or charging equipmentvia a power I/O component 940. Because the mobile device 900 can includeadditional and/or alternative components, the above embodiment should beunderstood as being illustrative of one possible operating environmentfor various embodiments of the concepts and technologies describedherein. The described embodiment of the mobile device 900 isillustrative, and should not be construed as being limiting in any way.

As used herein, communication media includes computer-executableinstructions, data structures, program modules, or other data in amodulated data signal such as a carrier wave or other transportmechanism and includes any delivery media. The term “modulated datasignal” means a signal that has one or more of its characteristicschanged or set in a manner as to encode information in the signal. Byway of example, and not limitation, communication media includes wiredmedia such as a wired network or direct-wired connection, and wirelessmedia such as acoustic, RF, infrared, and other wireless media.Combinations of any of the above should also be included within thescope of computer-readable media.

By way of example, and not limitation, computer storage media mayinclude volatile and non-volatile, removable and non-removable mediaimplemented in any method or technology for storage of information suchas computer-executable instructions, data structures, program modules,or other data. For example, computer media includes, but is not limitedto, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memorytechnology, CD-ROM, digital versatile disks (“DVD”), HD-DVD, BLU-RAY, orother optical storage, magnetic cassettes, magnetic tape, magnetic diskstorage or other magnetic storage devices, or any other medium which canbe used to store the desired information and which can be accessed bythe mobile device 900 or other devices or computers described herein,such as the computer system 800 described above with reference to FIG.8. For purposes of the claims, the phrase “computer-readable storagemedium” and variations thereof, does not include waves, signals, and/orother transitory and/or intangible communication media, per se.

Encoding the software modules presented herein also may transform thephysical structure of the computer-readable media presented herein. Thespecific transformation of physical structure may depend on variousfactors, in different implementations of this description. Examples ofsuch factors may include, but are not limited to, the technology used toimplement the computer-readable media, whether the computer-readablemedia is characterized as primary or secondary storage, and the like.For example, if the computer-readable media is implemented assemiconductor-based memory, the software disclosed herein may be encodedon the computer-readable media by transforming the physical state of thesemiconductor memory. For example, the software may transform the stateof transistors, capacitors, or other discrete circuit elementsconstituting the semiconductor memory. The software also may transformthe physical state of such components in order to store data thereupon.

As another example, the computer-readable media disclosed herein may beimplemented using magnetic or optical technology. In suchimplementations, the software presented herein may transform thephysical state of magnetic or optical media, when the software isencoded therein. These transformations may include altering the magneticcharacteristics of particular locations within given magnetic media.These transformations also may include altering the physical features orcharacteristics of particular locations within given optical media, tochange the optical characteristics of those locations. Othertransformations of physical media are possible without departing fromthe scope and spirit of the present description, with the foregoingexamples provided only to facilitate this discussion.

In light of the above, it should be appreciated that many types ofphysical transformations may take place in the mobile device 900 inorder to store and execute the software components presented herein. Itis also contemplated that the mobile device 900 may not include all ofthe components shown in FIG. 9, may include other components that arenot explicitly shown in FIG. 9, or may utilize an architecturecompletely different than that shown in FIG. 9.

Based on the foregoing, it should be appreciated that concepts andtechnologies for image prediction have been disclosed herein. Althoughthe subject matter presented herein has been described in languagespecific to computer structural features, methodological andtransformative acts, specific computing machinery, and computer-readablemedia, it is to be understood that the invention defined in the appendedclaims is not necessarily limited to the specific features, acts, ormedia described herein. Rather, the specific features, acts and mediumsare disclosed as example forms of implementing the claims.

The subject matter described above is provided by way of illustrationonly and should not be construed as limiting. Various modifications andchanges may be made to the subject matter described herein withoutfollowing the example embodiments and applications illustrated anddescribed, and without departing from the true spirit and scope of thesubject disclosure.

I claim:
 1. A method comprising: receiving, by an image predictionsystem comprising a processor, a training data set comprising aplurality of training images; defining, by the image prediction system,N-dimensional feature vectors corresponding to the plurality of trainingimages in the training data set; parameterizing, by the image predictionsystem, the N-dimensional feature vectors to obtain a plurality ofparameterized curves corresponding to the plurality of training imagesin the training data set; obtaining, by the image prediction system, asquare root velocity representation for each parameterized curve of theplurality of parameterized curves; rescaling, by the image predictionsystem, the plurality of parameterized curves to remove scalingvariability among the plurality of parameterized curves defining, by theimage prediction system, a pre-shape space for the plurality ofparameterized curves; and obtaining, by the image prediction system,shape space points pertaining to each parameterized curve of theplurality of parameterized curves on a shape space that inherits astructure from the pre-shape space.
 2. The method of claim 1, furthercomprising: collecting, by the image prediction system, a set of testimages within a time range; parameterizing, by the image predictionsystem, the set of test images to obtain a test parameterized curve; andobtaining, by the image prediction system, a new square root velocityrepresentation point for the test parameterized curve on the shapespace.
 3. The method of claim 1, further comprising: determining, by theimage prediction system, a mean of a plurality of training points on theshape space, wherein each of the plurality of training pointscorresponds to the square root velocity representation for eachcorresponding parameterized curve of the plurality of parameterizedcurves; defining, by the image prediction system, a tangent space aroundthe mean; warping, by the image prediction system, the plurality oftraining points from the shape space onto the tangent space usinginverse exponential mapping; performing, by the image prediction system,multi-variate statistical analysis on the tangent space to determine amost representative subset of the plurality of training points for agiven test point; and predicting, by the image prediction system, a testimage.
 4. The method of claim 1, further comprising: selecting, by theimage prediction system, a topic for prediction; considering, by theimage prediction system, a plurality of training points pertaining tothe topic for prediction; determining, by the image prediction system, amean of the plurality of training points on the shape space, whereineach of the plurality of training points corresponds to the square rootvelocity representation for each corresponding parameterized curve ofthe plurality of parameterized curves belonging to the topic selectedfor prediction; warping, by the image prediction system, the pluralityof training points from the shape space onto a tangent space defined atthe mean; performing, by the image prediction system, a principalcomponent analysis on the tangent space to yield a principal componentanalysis matrix; performing, by the image prediction system,dimensionality reduction by retaining eigenvectors with eigenvaluesgreater than 0.1; warping, by the image prediction system, a test pointonto the tangent space corresponding to the topic for selected forprediction; performing, by the image prediction system, dimensionalityreduction using the principal component analysis matrix learnt on thetangent space; considering, by the image prediction system, a nearesttraining neighbor based upon a distance of the eigenvectors; andpredicting, by the image prediction system, a test image based upon atest parameterized curve corresponding to the nearest training neighbor.5. The method of claim 1, further comprising: determining, by the imageprediction system, a mean of the plurality of training points on theshape space, wherein each of the plurality of training pointscorresponds to the square root velocity representation for eachcorresponding parameterized curve of the plurality of parameterizedcurves; warping, by the image prediction system, the plurality oftraining points from the shape space onto a tangent space defined at themean; performing, by the image prediction system, a principal componentanalysis on the tangent space; warping, by the image prediction system,a test point onto the tangent space; considering, by the imageprediction system, a nearest training neighbor based upon a distance ofthe eigenvectors; and predicting, by the image prediction system, a testimage based upon a test parameterized curve corresponding to the nearesttraining neighbor.
 6. The method of claim 1, further comprising:determining, by the image prediction system, a mean of the plurality oftraining points on the shape space; warping, by the image predictionsystem, the plurality of training points from the shape space onto atangent space defined at the mean; performing, by the image predictionsystem, dimensionality reduction using linear discriminant analysis toobtain reduced dimensional vectors; considering, by the image predictionsystem, a nearest training neighbor based upon a distance of the reduceddimensional vectors; and assigning, by the image prediction system, atopic label of the nearest training neighbor to a test point.
 7. Themethod of claim 1, further comprising: collecting, by the imageprediction system, a test image within a time range; parameterizing, bythe image prediction system, the test image to obtain a testparameterized curve; and obtaining, by the image prediction system, anew square root velocity representation point for the test parameterizedcurve on the shape space.
 8. A computer-readable storage mediumcomprising computer-executable instructions that, when executed by aprocessor, causes the processor to perform operations comprising:receiving a training data set comprising a plurality of training images;defining N-dimensional feature vectors corresponding to the plurality oftraining images in the training data set; parameterizing theN-dimensional feature vectors to obtain a plurality of parameterizedcurves corresponding to the plurality of training images in the trainingdata set; obtaining a square root velocity representation for eachparameterized curve of the plurality of parameterized curves; rescalingthe plurality of parameterized curves to remove scaling variabilityamong the plurality of parameterized curves; defining a pre-shape spacefor the plurality of parameterized curves; and obtaining shape spacepoints pertaining to each parameterized curve of the plurality ofparameterized curves on a shape space that inherits a structure from thepre-shape space.
 9. The computer-readable storage medium of claim 8,wherein the operations further comprise: collecting a set of test imageswithin a time range; parameterizing the set of test images to obtain atest parameterized curve; and obtaining a new square root velocityrepresentation point for the test parameterized curve on the shapespace.
 10. The computer-readable storage medium of claim 8, wherein theoperations further comprise: determining a mean of a plurality oftraining points on the shape space, wherein each of the plurality oftraining points corresponds to the square root velocity representationfor each corresponding parameterized curve of the plurality ofparameterized curves; defining a tangent space around the mean; warpingthe plurality of training points from the shape space onto the tangentspace using inverse exponential mapping; performing multi-variatestatistical analysis on the tangent space to determine a mostrepresentative subset of the plurality of training points for a giventest point; and predicting a test image.
 11. The computer-readablestorage medium of claim 8, wherein the operations further comprise:selecting a topic for prediction; considering a plurality of trainingpoints pertaining to the topic for prediction; determining a mean of theplurality of training points on the shape space, wherein each of theplurality of training points corresponds to the square root velocityrepresentation for each corresponding parameterized curve of theplurality of parameterized curves belonging to the topic selected forprediction; warping the plurality of training points from the shapespace onto a tangent space defined at the mean; performing a principalcomponent analysis on the tangent space to yield a principal componentanalysis matrix; performing dimensionality reduction by retainingeigenvectors with eigenvalues greater than 0.1; warping a test pointonto the tangent space corresponding to the topic for selected forprediction; performing dimensionality reduction using the principalcomponent analysis matrix learnt on the tangent space; considering anearest training neighbor based upon a distance of the eigenvectors; andpredicting a test image based upon a test parameterized curvecorresponding to the nearest training neighbor.
 12. Thecomputer-readable storage medium of claim 8, wherein the operationsfurther comprise: determining a mean of the plurality of training pointson the shape space, wherein each of the plurality of training pointscorresponds to the square root velocity representation for eachcorresponding parameterized curve of the plurality of parameterizedcurves; warping the plurality of training points from the shape spaceonto a tangent space defined at the mean; performing a principalcomponent analysis on the tangent space; warping a test point onto thetangent space; considering a nearest training neighbor; and predicting atest image based upon a test parameterized curve corresponding to thenearest training neighbor.
 13. The computer-readable storage medium ofclaim 8, wherein the operations further comprise: determining a mean ofthe plurality of training points on the shape space; warping theplurality of training points from the shape space onto a tangent spacedefined at the mean; performing dimensionality reduction using lineardiscriminant analysis to obtain reduced dimensional vectors; consideringa nearest training neighbor based upon a distance of the reduceddimensional vectors; and assigning a topic label of the nearest trainingneighbor to a test point.
 14. The computer-readable storage medium ofclaim 8, wherein the operations further comprise: collecting a testimage within a time range; parameterizing the test image to obtain atest parameterized curve; and obtaining a new square root velocityrepresentation point for the test parameterized curve on the shapespace.
 15. A system comprising: a processor; and memory that storesinstructions that, when executed by the processor, cause the processorto perform operations comprising receiving a training data setcomprising a plurality of training images, defining N-dimensionalfeature vectors corresponding to the plurality of training images in thetraining data set, parameterizing the N-dimensional feature vectors toobtain a plurality of parameterized curves corresponding to theplurality of training images in the training data set, obtaining asquare root velocity representation for each parameterized curve of theplurality of parameterized curves, rescaling the plurality ofparameterized curves to remove scaling variability among the pluralityof parameterized curves, defining a pre-shape space for the plurality ofparameterized curves, and obtaining shape space points pertaining toeach parameterized curve of the plurality of parameterized curves on ashape space that inherits a structure from the pre-shape space.
 16. Thesystem of claim 15, wherein the operations further comprise: collectinga set of test images within a time range; parameterizing the set of testimages to obtain a test parameterized curve; and obtaining a new squareroot velocity representation point for the test parameterized curve onthe shape space.
 17. The system of claim 15, wherein the operationsfurther comprise: determining a mean of a plurality of training pointson the shape space, wherein each of the plurality of training pointscorresponds to the square root velocity representation for eachcorresponding parameterized curve of the plurality of parameterizedcurves; defining a tangent space around the mean; warping the pluralityof training points from the shape space onto the tangent space usinginverse exponential mapping; performing multi-variate statisticalanalysis on the tangent space to determine a most representative subsetof the plurality of training points for a given test point; andpredicting a test image.
 18. The system of claim 15, wherein theoperations further comprise: selecting a topic for prediction;considering a plurality of training points pertaining to the topic forprediction; determining a mean of the plurality of training points onthe shape space, wherein each of the plurality of training pointscorresponds to the square root velocity representation for eachcorresponding parameterized curve of the plurality of parameterizedcurves belonging to the topic selected for prediction; warping theplurality of training points from the shape space onto a tangent spacedefined at the mean; performing a principal component analysis on thetangent space to yield a principal component analysis matrix; performingdimensionality reduction by retaining eigenvectors with eigenvaluesgreater than 0.1; warping a test point onto the tangent spacecorresponding to the topic for selected for prediction; performingdimensionality reduction using the principal component analysis matrixlearnt on the tangent space; considering a nearest training neighborbased upon a distance of the eigenvectors; and predicting a test imagebased upon a test parameterized curve corresponding to the nearesttraining neighbor.
 19. The system of claim 15, wherein the operationsfurther comprise: determining a mean of the plurality of training pointson the shape space, wherein each of the plurality of training pointscorresponds to the square root velocity representation for eachcorresponding parameterized curve of the plurality of parameterizedcurves; warping the plurality of training points from the shape spaceonto a tangent space defined at the mean; performing a principalcomponent analysis on the tangent space; warping a test point onto thetangent space; considering a nearest training neighbor based upon adistance of the eigenvectors; and predicting a test image based upon atest parameterized curve corresponding to the nearest training neighbor.20. The system of claim 15, wherein the operations further comprise:determining a mean of the plurality of training points on the shapespace; warping the plurality of training points from the shape spaceonto a tangent space defined at the mean; performing dimensionalityreduction using linear discriminant analysis to obtain reduceddimensional vectors; considering a nearest training neighbor based upona distance of the reduced dimensional vectors; and assigning a topiclabel of the nearest training neighbor to a test point.